Dynamics of the vortex line density in superfluid counterflow turbulence

Describing superfluid turbulence at intermediate scales between the inter-vortex distance and the macroscale requires an acceptable equation of motion for the density of quantized vortex lines $\cal{L}$. The closure of such an equation for superfluid inhomogeneous flows requires additional inputs besides $\cal{L}$ and the normal and superfluid velocity fields. In this paper we offer a minimal closure using one additional anisotropy parameter $I_{l0}$. Using the example of counterflow superfluid turbulence we derive two coupled closure equations for the vortex line density and the anisotropy parameter $I_{l0}$ with an input of the normal and superfluid velocity fields. The various closure assumptions and the predictions of the resulting theory are tested against numerical simulations.Comment: 7 pages, 5 figure

Thermodynamics and kinetics of solids fragmentation at severe plastic deformation

The approach of nonequilibrium evolution thermodynamics earlier offered is developed. It helps to describe the processes of defect formation within the adiabatic approximation. The basic equations system depends on the initial defects distribution (dislocations and grain boundaries). The phase diagram is determined with the domains of the realization of different limiting structure types. The interaction effect of several defect types on the formation of a limiting structure is investigated in terms of the internal energy. The conditions of the formation of two limiting structures are found. The kinetics of the steady-state values establishment of the defects density is investigated within the scope of the adiabatic approximation. The dislocations density change follows the evolution of the grain boundaries density in this approach. It is shown that grain sizes, in limiting structures, decrease with an increase of the elastic strains.Comment: 14 pages, 6 figure